16100lectre36_cj

16100lectre36_cj - Subsonic Small Disturbance Potential...

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Subsonic Small Disturbance Potential Flow 1. j v i u V V v v v ˆ ) ˆ ( + + = where 1 | ˆ ˆ | 2 2 2 << + V v u 2. = + φ ˆ ˆ ˆ ˆ j v i u v v perturbation potential y v x u = = ˆ ˆ ˆ ˆ 3. small-disturbance (?) and bc’s= 0 ˆ ˆ ) 1 ( 2 2 2 2 2 = + y x M BC: ) ( ) 0 , ( ˆ x dx dy V x v c = where = c y camber line Note: this eqn and bc are valid for subsonic and supersonic flow. Also note , = = V u q p p C u p ˆ 2 4. For subsonic flow, we utilize the following mathematical transformation: Define: 2 1 = M β η ξ ˆ = = = y x ) ( ) 0 , ( 0 2 2 2 2 dx dy V c = = + The implications are that the subsonic compressible flow around an airfoil can be related to the incompressible ) 0 ( = M flow about the airfoil. small disturbances are assumed Same eqn Same bc 0 = M 0 ˆ ˆ 2 2 2
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.

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16100lectre36_cj - Subsonic Small Disturbance Potential...

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